For system (REF ) we have the following results.
 
All solutions of (REF ) which are initiated in the first quadrant are bounded and eventually end up in \(\Phi =\lbrace \left(u,v\right),\ 0<u\le 1,\ 0\le v\le 1\rbrace \) .


Arancibia-Ibarra et al. proved that all the solution of system (REF ) with \(M>0\)  are bound and eventually end up in \(\Phi \)  [1]}. As all the conditions used to prove Theorem 2 does not depend on the parameter \(M\)  we can conclude that for system (REF ) with \(M<0\)  all the solutions initiated in \(\Omega \)  are also bounden and end up in \(\Phi \) .
